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Math 102: Foundation Of Mathematics 2Nd Trimester 2014 Question Paper
Math 102: Foundation Of Mathematics 2Nd Trimester 2014
Course:Bachelor Of Business Information Technology
Institution: Kenya Methodist University question papers
Exam Year:2014
FOUNDATIONS OF MATHEMATICS (MATH 102) 2nd trimester 2014
KENYA METHODIST UNIVERSITY
END OF 2'ND 'TRIMESTER 2014 (FT) EXAMINATION
FACULTY : SCIENCE & TECHNOLOGY
DEPARTMENT : PURE AND APPLIED SCIENCES
UNIT CODE : MATH 102
UNIT TITLE : FOUNDATION OF MATHEMATICS
TIME : 2 HOURS
INSTRUCTIONS
Answer question one and any other two questions
Question One (COMPULSORY)
Define a set
(2 Marks)
Let A={3,1,0} and B={2,0,8,7} be sets, determine the Cartesian product of A and B (AxB)
(6 marks)
Given the set A and B above (b) and given the following relations from A into B as
R1 = {1,8}
R2 = {(1,2), (0,8), (3,7)}
R3 = {(0,2), (0,8), (3,2), (1,2)}
R4 = {(1,2), (0,8), (3,7)}
R5 = {(3,2), (3,0), (3,8), (3,7)}
Define what meant by a function
Identify functions from the relations (R1, R2, R3, R4 and R5 above
(5 Marks)
Solve for y in ½ log5(x+6)-log2x=0
(4 Marks)
Find the mid-point between the points (-3,7) and (7,3)
(2 Marks)
Given the functions f(x)=3x-6 and g(x)=2x3+5 find
g-1(x)
(3 Marks)
fg(x)
(3 Marks)
gof(x)
(3 Marks)
A straight line passes through the point (-2,3) and has gradient ½. Find the equation of the line
(2 Marks)
Question Two (20 marks)
Define the following terms
Universal set
(2 Marks)
Empty set
(2 marks)
Power set
(2 Marks)
If A={1,2,3} find
P(A)
(3 Marks)
n(A)
(2 Marks)
nP(A)
(2 Marks)
If A={x:x=3} and B={x: x < 5} find
A? B
(2 Marks)
A n B
(2 Marks)
A – B
(3 Marks)
Question Three (20 marks)
Find the first 5 terms of the sequence whose nth terms are
an = n2-1
(2 marks)
an = (n+2)/(n+2)
(2 Marks)
(i) Find the sum S10 and common difference d of the sequence whose 1st term a1=1 and 10th term a10=19.
(4 marks)
Write the first four terms of the sequence then find a10 and S10 given that a1 = 5 and d=3
(5 Marks)
Given that a1=3, r=4 find S5 for the geometric sequence
(3 Marks)
If the statement P is "5 > 3" and q is "Meru is in Kenya," find the truth value of the compound statement +Pv(?+q)
(4 Marks)
Question Four (20 Marks)
Write the general form of the equation of a line passing through the points (3, -4) and (6,10
(4 Marks)
Determine whether the following lines are parallel or perpendicular
(5 marks)
15x+3y-7=0 and 5x – 25y – 8 =0
Show that ¬(pvq) v (¬pnq) = ¬p
(5 Marks)
The sum of the 1st 10 terms of an AP is 120. The sum of the next 10 terms is 320. Calculate:
The 1st term
(3 Marks)
The common difference
(3 marks)
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